Related papers: Statistical Inference in High-dimensional Poisson …

We study a regression model with a huge number of interacting variables. We consider a specific approximation of the regression function under two ssumptions: (i) there exists a sparse representation of the regression function in a…

Researchers are often interested in understanding the relationship between a set of covariates and a set of response variables. To achieve this goal, the use of regression analysis, either linear or generalized linear models, is largely…

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…

In a variety of application areas, there is a growing interest in analyzing high dimensional sparse count data, with sparsity exhibited by an over-abundance of zeros and small non-zero counts. Existing approaches for analyzing multivariate…

We propose an extensive simulation study to compare some variable selection procedures in a high-dimensional framework. Assuming that the relationship between the actives variables and the response variable is linear, the high-dimensional…

The method of instrumental variables provides a fundamental and practical tool for causal inference in many empirical studies where unmeasured confounding between the treatments and the outcome is present. Modern data such as the genetical…

We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…

The debiased estimator is a crucial tool in statistical inference for high-dimensional model parameters. However, constructing such an estimator involves estimating the high-dimensional inverse Hessian matrix, incurring significant…

We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any…

Finite mixture regression models are useful for modeling the relationship between response and predictors, arising from different subpopulations. In this article, we study high-dimensional predic- tors and high-dimensional response, and…

This article deals with the analysis of high dimensional data that come from multiple sources (experiments) and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may…

The Poisson distribution is the default choice of likelihood for probabilistic models of count data. However, due to the equidispersion contraint of the Poisson, such models may have predictive uncertainty that is artificially inflated.…

In genetic studies, not only can the number of predictors obtained from microarray measurements be extremely large, there can also be multiple response variables. Motivated by such a situation, we consider semiparametric dimension reduction…

Consider an unlimited homogeneous medium disturbed by points generated via Poisson process. The neighborhood of a point plays an important role in spatial statistics problems. Here, we obtain analytically the distance statistics to $k$th…

Being in the era of big data, modeling and prediction of count data have become significantly important in many fields including health, finance, social, etc. Although linear Poisson regression has been widely used to model count and rate…

Across many scientific fields, measurements often represent the number of times an event occurs. For example, a document can be represented by word occurrence counts, neural activity by spike counts per time window, or online communication…

We develop a dimension reduction framework for data consisting of matrices of counts. Our model is based on assuming the existence of a small amount of independent normal latent variables that drive the dependency structure of the observed…

Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…

The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In…

In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…